The traveling salesman problem with distances one and two
Mathematics of Operations Research
A linear time algorithm for finding tree-decompositions of small treewidth
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
An improved approximation ratio for the minimum latency problem
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
P-Complete Approximation Problems
Journal of the ACM (JACM)
The prize collecting Steiner tree problem: theory and practice
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
The Minimum Latency Problem Is NP-Hard for Weighted Trees
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Improved Approximation Algorithms for Metric Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
On Salesmen, Repairmen, Spiders, and Other Traveling Agents
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation Schemes for Minimum Latency Problems
SIAM Journal on Computing
Paths, Trees, and Minimum Latency Tours
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximate k-MSTs and k-Steiner trees via the primal-dual method and Lagrangean relaxation
Mathematical Programming: Series A and B
Facility location and the analysis of algorithms through factor-revealing programs
Facility location and the analysis of algorithms through factor-revealing programs
A Faster, Better Approximation Algorithm for the Minimum Latency Problem
SIAM Journal on Computing
Importance sampling via load-balanced facility location
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Improved genetic algorithm for minimum latency problem
Proceedings of the 2010 Symposium on Information and Communication Technology
Improved Approximation Algorithms for Prize-Collecting Steiner Tree and TSP
SIAM Journal on Computing
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The minimum latency problem (MLP) is a well-studied variant of the traveling salesman problem (TSP). In the MLP, the server's goal is to minimize the average latency that the clients experience prior to being served, rather than the total latency experienced by the server (as in the TSP). The MLP sometimes goes by other names, such as the traveling repairman problem, or the deliveryman problem. Unlike most combinatorial optimization problems, the MLP is NP-hard even on trees (Sitters, 2001). Our main result is an improved approximation algorithm for the MLP on trees, upon which we build improved approximation algorithms for a much wider class of graphs. The MLP on trees is interesting for several reasons. First, many of the aspects that make the problem difficult on general graphs are already present in the tree case. Second, all existing approximation algorithms for general graphs are built on approximation algorithms for the tree case. Third, there has been no improvement for the tree case since the 3.59-approximation of Goemans and Kleinberg, first introduced 14 years ago in 1996. Fourth, in the intervening period, the best ratio for general metrics has been improved to match the 3.59 for trees (Chaudhuri et al., 2003). In this paper, we improve the approximation ratio for trees to 3.03. In fact, our 3.03-approximation algorithm works for any class of graphs in which the related prize-collecting stroll (PCS) problem is solvable in polynomial time, such as graphs of constant treewidth. More generally, for any class of graphs that admit a Lagrangian-preserving β-approximation algorithm, we can use this algorithm as a black box to achieve a 3.03β-approximation for the MLP. Sadly, this does not immediately improve the ratio of 3.59 for general graphs, because the current best value of β for that case is 2. One interesting piece of our analysis is the solution of an infinite-dimensional linear program, used to analyze a finite-dimensional factor-revealing linear program (FRLP). We believe that our methods may hold promise for easing the analysis of other FRLPs encountered in the literature.